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| segment whose end points are ON the circle |
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| equation used to find the number of diagonals in a polygon |
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| a line that intersects a circle twice |
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| angle measure = 1/2 (x+y) |
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| equation used to find the angle formed when 2 chords or secants intersect INSIDE the circle |
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| angle measure = 1/2 (x-y) |
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| equation used to find the angle formed when 2 chords or secants intersect OUTSIDE the circle |
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| equation used to find the angle measure of an inscribed angle, where the vertex and the end points intersect the circle. (or angle measure/2) |
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| pythagorean thereom. used to find sides or a 90 degree right triangle when 2 sides are known. |
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| used when a triangle or trapezoid is split. used to find one of the split sides. |
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| height of line perpendicular to hypotenuse |
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if a/g=g/b, then the geometric mean is:
g=√ab
ex. x/5=45/x ; geom. mean= √x2=√225 (x squared) |
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(sin)=SOH
sin<(angle)=opposite/hypotenuse |
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(cos)=CAH
cos<(angle)=adjacent/hypotenuse |
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(tan)=TOA
tan<(angle)=opposite/adjacent |
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| a comparison of 2 values using division |
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| an equation where 2 ratios are set equal to eachother |
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| AA and SAS congruence thereoms |
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Definition
AA: if two angles of a triangle are 2 angles of another triangle, then the 2 triangles are similar.
SAS: if 2 sides of a triangle are proportional to 2 sides of another triangle and the angles in between are congruent, then the triangles are similar. |
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| lengths, perimeters, etc. |
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| areas, lateral areas, surface areas, etc. |
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| Law of Ruling our Possibilities |
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| when statement p or statement q is true AND q is not true, then p is true. |
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| If both p->q are true, then you can conclude that q is true. |
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True or False:
If p->q is true, and q is true, then you can conclude that p is true. |
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| If both p->q are true and q->r is true, then you can conclude that p->r is true. |
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If p->q is true, then not-q -> not-p is true.
If p->q is false, then not-q -> not-p is false. |
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| Law of Indirect Reasoning |
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Definition
Showing all the possibilities and show that only one works.
Steps:
1. Write "suppose the (opposite)" of what you're trying to prove
2. Produce a contradiction
3. End with "therefore..." (what you're trying to prove) (3 dotted triangle symbol = therefore) |
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Definition
d=√(y1-y2)2+(x1-x2)2
to find the distance between two points on a graph |
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| Equation for a circle with center (h,k) and radius 'r' |
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| midpoint formula on a number line |
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| Midpoint of (x1,y1) and (x2,y2) on a coordinate plane |
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(x1+x2 , y1+y2)
_______ ______
2 2 |
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| d=√(y1-y2)2 + (x1-x2)2 + (z1-z2)2 |
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r2= (x-h)2 + (y-k)2 + (z-j)2
r=radius
(h,k,j)=center |
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Definition
(x1+x2 , y1+y2 , z1+z2)
_______ _______ _______
2 2 2 |
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| 2d for Diagonal of a rectangle |
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| the boundary of a 3d figure |
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| has a top and a bottom to it. bases are congruent and parallel to eachother. like taking a 2d shape and stacking it. ex. deck o' cards |
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| the side is perpendicular to base. |
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| the side is on a diagonal and not perpendicular to base. |
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| every lateral face is perpendicular to bases. |
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| when lateral face is not perpendicular to bases. |
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| bases are regular polygons (automatically can assume it's a 'right' shape) |
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| informal name for a 'right' rectangular prism |
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